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Award for Chemnitz Mathematics

Joseph F. Traub Prize awarded to Prof. Dr. Tino Ullrich - One of the highest awards in the "Information Based Complexity" (IBC) community

The Joseph F. Traub Prize is one of the highest awards in the Information Based Complexity (IBC) mathematical community. It is endowed annually by the American computer scientist and IBC pioneer Prof. Joseph Traub (Columbia University). After his death in 2015, this was continued by his widow Pamela McCorduck, a well-known non-fiction author on the topic of artificial intelligence. This year, the award went to Prof. Dr. Tino Ullrich, holder of the Professorship of Applied Analysis at Chemnitz University of Technology. Tino Ullrich received the award during an international online workshop on “Sampling Recovery and Related Problems”, which he co-organized and which took place from May 3 to May 7, 2021.

Prof. Ullrich accepted the award from Prof. Dr. E. Novak, editor in chief of the Journal of Complexity and chair of the award committee. The prize is endowed with $3,000 and went equally to Dr. Mario Ullrich (Johannes Kepler University Linz), Prof. Vladimir Temlyakov (University of South Carolina) and Prof. Dr. Tino Ullrich (Chemnitz University of Technology).

The honor is a result of Prof. Ullrich and his research group’s outstanding contribution to the field of approximation theory related to complexity theory and machine learning. The special problem is of fundamental complexity-theoretic nature. It is about the optimal reconstruction of multivariate functions from sparse information. Since in various practical applications in machine learning or signal processing, only a few samples are available or these can only be computed "expensively", one tries to reduce their number by clever selection of "measurements." Such a reduction is not arbitrarily possible and is limited by the number of degrees of freedom in the system. Prof. Ullrich's team has now succeeded in making a significant advance by building a bridge to a famous problem from pure mathematics (quantum mechanics/operator theory), the Kadison-Singer conjecture. This conjecture was solved in 2015 by Marcus, Spielman, and Srivastava. This showed that, theoretically, far fewer samples are sufficient than previously thought to compute a good reconstruction. There remains a very small dimension-independent "logarithmic gap" to the best possible bound and the question whether the reconstruction from discrete samples is de facto more difficult than the optimal reconstruction from the "first" Fourier coefficients of the Fourier series expansion. With the Fourier series expansion of a periodic, piece-wise continuous function, a function series of sine and cosine functions is designated. By a “natural truncation”, one receives the optimal approximation in most cases.

Prof. Ullrich's long-time colleague Prof. Vladimir Temlyakov from the University of South Carolina and Moscow State University was also involved here and organized the current online workshop together with Prof. Ullrich. "I was very happy about this appreciation of my work and personally feel it as an extraordinary honor. Of course, the contribution of the working group should not go unmentioned here. In addition, it gives me a lot of motivation to continue tackling the often very difficult mathematical problems that we address in our research," says Prof. Ullrich about his success.

The excellent results achieved by Prof. Ullrich and his team were also the subject of discussion at the online workshop that has now taken place. Internationally high-ranked  experts in complexity and approximation theory participated. The workshop was jointly organized by Chemnitz University of Technology and Lomonosov Moscow State University.

Multimedia: In the podcast series TUCpersönlich (german) Prof. Dr. Tino Ullrich talks about his fascination for numbers and what a challenge a professorship is.

(Author: Matthias Fejes / Translation: Chelsea Burris)

Matthias Fejes
20.05.2021

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